Are Dreams a Form of Backpropagation?
This is a very interesting question and also an important one for AI. All the current Deep Learning successes are built on the effectiveness of backprop, so what if it doesn't play a role in the only examples of intelligence currently around?

It makes a lot of sense for the brain to employ some form of backprop, because that would allow it to create low-level features in a way most conductive for the high-level features that finally give rise to intelligent behavior. And if the brain employs backprop, dreams are a logical candidate.

Of course the problem here is that the brain doesn't calculate and propagate gradients, so the question is whether the backpropagation algorithm can somehow be implemented with the biological constraints in mind, such as the locality of neural computation and the non-symmetrical feedback connections.

It turns out this is actually possible, as explained in these talks by Hinton and Bengio. Symmetrical feedback connections (and in fact continually updated feedback connections) aren't necessary for backpropagation, however unintuitive this may seem. And backpropagation can be emulated with a form of temporal difference learning, that is plausible within biological constraints. 

Of course this doesn't conclusively answer the question, but it certainly makes the possibility much more plausible than a priori assumed.